A Seamless Whole Speed Range Control of

Interior PM Synchronous Machine withoutPosition Transducer

Roman Filka*, Peter Balazovic*, Branislav Dobruckyt* Freescale Semiconductor, 1. Maje 1009, Roznov p. Radhostem, Czech Republic

t University of Zilina/Department of Electrical Engineering, Univerzitna' 1, 010 26 Zilina, Slovakia

Abstract- This paper presents a complex solution for wholespeed range sensorless control of interior permanent magnetsynchronous motor (IPMSM) drives. To cover an entirespeed range of IPMSM without position transducer,different sensorless techniques must be employed. Designand implementation of sensorless techniques for differentoperating speeds are described in this paper. Presentedapplication has been implemented including the highfrequency (hf) injection method and extended back EMFstate observer on a single chip solution of DSC56F8300series without any additional supportive circuitry.

I. INTRODUCTIONAn important factor for using sensorless control in the

drive applications is to optimize the total cost performanceratio of the overall drive cost. The systems should be lessnoisy, more efficient, smaller and lighter, more advancedin function and accurate in control with a low cost. Toachieve efficient control of AC machines, knowledge ofrotor position is essential. Different types of mechanicalposition transducers can be used to measure the rotorposition directly. However solution with such transducerintroduces additional cost, therefore alternative means ofobtaining rotor position is highly desirable.

Sensorless control of AC machines has become afrequently discussed topic at engineering conferences.Many researchers and scientists have published papers onthis topic but there are only a few articles that discusscomplex implementation of the algorithms into a singleapplication covering all operating conditions. One solutionto sensorless control of the motor drive in applicationssuch as air-condition units, fans, compressors is to use abrushless DC motor (BLDC). These motors havetrapezoidal back-EMF, because of geometricalarrangement of the magnets in the rotor; therefore six stepcommutation control is sufficient [1]. Driving motor in sixstep commutation allows for observation of back-EMFzero crossing, since there is always an instant in switchingsequence of the inverter, when both switches in one of theinverter leg do not conduct the current. Knowing the pointof back-EMF zero crossing a subsequent commutationsequence can be calculated, thus allowing BLDC motor tooperate without position transducer. Six step commutationcontrol ofBLDC however, has several drawbacks; such aslow efficiency, higher audible noise and lower developedtorque when compared to sinusoidal control ofPMSM. Toincrease efficiency of the drive, sinusoidal control isneeded [1]. Here, all three phases of the inverter areconstantly conducting current making observation of

back-EMF zero crossing impossible. Therefore morecomplex sensorless algorithms must be employed.

Sensorless algorithms for sinusoidal control of ACmachines can be broadly divided into two major groups;1.) Those that utilize magnetic saliency for tracking rotorposition [2]-[12] and 2) those that estimate rotor positionfrom calculating motor model [8],[13]-[16]. The later,requires accurate knowledge of phase voltages and currentfor proper functionality. At low speeds, phase voltagereference and measured phase current are low, making itvery difficult to separate from noise. Also distortion byinverter non-linearities and model parameter deviationbecomes significant with decreasing speed. Thereforemethods based on motor model are not suitable for lowrotor speeds. For start-up and low speeds, additionalcarrier signal superimposed to the main excitation isrequired. This carrier signal adds needed excitation to themotor at low and zero speed, and its back analysis canprovide a viable means of obtaining information aboutrotor position. The carrier injection methods however,require a certain amount of saliency present in the motor[3]. In IPMSM this saliency results from inductancevariation [1] as is explained later in the paper. On theother hand, at high speeds the amplitude of back EMF isbig enough for motor model and angle tracking observerto work properly, therefore no additional signal isrequired. In fact, additional hf signal deteriorates trackingaccuracy of the angle tracking observer. Thereforeinjection of hf signal is not desired for high speedoperation. It is obvious, that in order to achieve full speedrange sensorless operation of IPMSM, both techniqueshave to be employed, each covering different operationalspeed ranges. This requires algorithm that will ensureseamless blending of the estimates throughout the entirespeed range.

The proposed solution is based on field oriented controlof IPMSM with implemented speed control loop. Thisincludes inner current control loop with implementeddecoupling of cross-coupled variables achieving goodtorque control performance. To maximize converterefficiency and minimize its rating, current loop isdesigned with maximum torque/ampere criteria [1].

II. IPMSM CHARACTERIZATION

A. Motor DescriptionMathematical model of IPM synchronous motor in

synchronous reference frame is described as follows

1-4244-0121-6/06/$20.00 C2006 IEEE 1008 EPE-PEMC 2006, Portoro2, Slovenia

Ud 1 F± Lds LqW ]Fd od = Rs d + qCL)L 'd + 1YPMrCOI[ U 'qjLi -LdWtr LqS iLq ±JPWLI

wheres - differential operator;Udq - stator voltages in synchronous reference frame;

'dq - stator currents in synchronous reference frame;Ldq - direct and quadrature inductances;

C - rotor speed;7//PM - permanent magnet flux;Torque developed by the IPM synchronous motors as

described by (2), can be divided into two components.First component of the torque is created by contribution ofthe PM field 7/PM and is called synchronous torque.Second component, referred to as reluctance torque, arisesdue to rotor saliency, where the rotor tends to align withthe minimum reluctance.

3

=P /PM iq +±(Ld Lq )idiq) (2)e2 \

wherep - number ofpole pairsIPM motors have the permanent magnets buried inside

the rotor, which makes them salient pole machines withsmall effective air-gap. Reluctance in q-axis direction issmaller than that one in d-axis, resulting in q-axisinductance bigger than d-axis; Ld < Lq . Therefore in orderto develop maximal torque according to (2), reluctancetorque should be utilized i.e. id current has to be adjustedto negative values, weakening the resulting magnetic field.On the other hand, the armature reaction effects aredominant, due to small effective air-gap, resulting insaturation of q-axis inductance according to level ofapplied load. This phenomenon is particularly important,because magnetic saliency decreases proportionally withsaturated inductance and disappearing completely atcertain load level. Furthermore under load the torquecurrent in q-axis winding creates a term G/'pmiq causingair-gap flux distribution to move towards direction of q-axis. Since the HF signal injection sensorless algorithmestimates the position of saliency rather than the positionof rotor itself, this phenomenon has to be accounted for inthe final application.

B. High Frequency ImpedanceIn order to verify presence of magnetic saliency at high

frequencies (hj), hf impedance measurements were carriedout, as proposed by [4]. In these measurements, rotor ismechanically locked to prevent current signals distortion.HF signal of 50V/500Hz is injected in dm - axis of themeasurement dm-qm reference frame. This frame is shiftedfrom actual rotor d-q frame by angle_offset. Offsetting themeasurement frame will ensure correct alignment of theframes anytime the measurement is repeated. Sinceangle offset is varied ±180 deg. electrical, at 90 deg. idmwill correspond to iqm. Therefore to suppress DC offset ofthe idm current under load, Ist order high pass filter withcut-off frequency 10Hz is used. Block diagram showing

the hfimpedance measurement algorithm as implemented(1) on Digital Signal Controller is depicted on Fig. 1.

Fig. 1. Block diagram ofHF impedance measurement.

Obtained measurement results are shown on Fig. 2,where resulting impedance is plotted as a function ofangle_offset and load level. It can be seen from Fig. 2, thatthe saliency moves towards the direction of q-axis anddisappears with increasing load level as assumed insection II. A. Saliency disappearing with increasing loadwill cause eventual failure of sensorless algorithm basedon saliency tracking. This can be avoided by propercompensation action in d-axis current [4], which howeverwill introduce additional losses in the motor and decreasethe efficiency of the control loop.

-200450 -100 X50 0 m0 0 4J 200

aile et deg

Fig. 2. High Frequency impedances as a function of difference betweenmeasurement and actual rotor reference frames and applied load.

III. DESIGN OF SENSORLESS CONTROL FOR IPMSM

A. Initial Position Detection andLow Speed SensorlessControlAs with any other synchronous motor, the first problem

to overcome in FOC is the motor start-up. In contrast withAC induction motor where rotor flux is basically createdfrom the stator, in IPM motor the rotor flux is created bypermanent magnets present in the rotor. In order to be ableto use FOC, position of this rotor flux has to be knownprior to any control action. In conventional IPM controlwith an encoder as position transducer, initial position isset by applying DC voltage in one motor phase, whichcreates a magnetic pole attracting opposite pole of rotormagnets (alignment process). This process unavoidablygenerates often unwanted rotor movements. Sensorless

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algorithm based on injection of pulsating hf signal insynchronous frame can be used to estimate the position ofrotor at start-up. This sensorless approach is physicallybased on property of d and q axes flux being decoupled[3]. Therefore if an estimated d-q reference frame isdefined and not precisely aligned with a real rotord-q reference frame, then by applying flux vector atknown carrier frequency for example in the d axis,current at carrier frequency can be observed in the qc axis.This current is directly proportional to the misalignmentangle of the estimated and rotor reference frame.Therefore changing the position of estimated frame suchthat this qc axis current is zero or minimal, will allow fortracking of real rotor i.e. saliency position.

Considering high frequency signals, motor model from(1) can be rewritten into estimated reference frame (3). Inthis hfIPM synchronous motor model, voltage drop acrossthe stator resistance and back-EMF components can beneglected.

ir

1s(twn- ._ t)stim

Oestim

PCtzf

Fig. 3. Saliency tracking observer (STO); as used for rotor positionestimation at zero and low speeds.

Output of the PI controller represents the estimatedspeed, thus its integration yields position of the estimatedreference frame. Such structure acts as a phase lockedloop and its schematic block diagram is depicted on Fig.3.

Ud1 FZi+AZ cos(20,,)L q] L AZ sin(20,,) Z-

ere

Zd +Zq Zd -Z

2 ' 2

-AZsin(2Q0,) 1F'dl

-AZ cos(20, )iq]

£9rr £9ot est

Udq - stator voltages in estimated frame;

-dq stator currents in estimated frame;0rot - rotor position;

Oest - estimated position;

0err - position error;

Applying hf signal Uhf = Ur sin(wohft) in d-axis of hfmodel of (3), will result in hf currents

-Z -AZcos(2O0ri)]L'qj 60Chf ZdZq hfL_

AZsin(2Oe,r)

Fig. 4. Saliency tracking observer; initial position alignment.

Fig. 4 demonstrate experimental results of initialSaliency Tracking Observer (STO) alignment, which isused for start-up rotor position detection. The experimentis carried out with rotor manually rotated to arbitraryposition and then running STO alignment process.

(5)

After filtering and demodulation, iq current is describedas

iq =_ 2 thZAZ sin(20r)q

(6)

The relationship between iq and estimated positionerror from (6) suggest to use a controller capable ofdriving its output such that iq current will remain zero.

This can be a standard proportional-integrational (PI)controller.

Fig. 5. Position error during reversal at 30rpm. IPMSM operated in fullsensorless speed FOC.

Position error during speed reversal at 30 rpm isdepicted on Fig. 5. Here the motor is operated in speedFOC with position and speed feedback provided by STO,i.e. full sensorless mode. Rotor position from encoder isused only for comparison with estimated position.Experimental results of low speed full sensorless controlwith speed reversal under different load conditions areshown on Fig. 6, and Fig. 7. Rotor position informationfrom encoder is not used in these experiments.

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wh(

(3)

(4)

,,,,,,,,,,,,,,,,, r0003MuNCO,,l,iwp,,,axis

UREL.\0re

UL

10 2M 0mirne ljse;

4b 4s 0

Fig. 6. Low speed full sensorless FOC, with speed reversal ±30 rpmunder no load.

Spe et6 enid Sp~e&Wu arpWm

=.77- I [ l

s:810 20 25 3Tie jsec

lre uire

4s$ 45 5

Fig.Vecto diagram of salient-pole m-axis

Fig. 8. Vector diagram of salient-pole machine.

The vector representation of given equation (7) isdisplayed in Fig. 8. Unfortunately, the computation ofposition dependent information which is contained in twounknown voltage vectors conventional UE, and URELmakes difficulties to assess it. However, there has beenproposed [13] a simple way to resolve this problem byeliminating the 20e term in (7) using purely mathematicalmethod. Here is described a mathematical model ofinterior PMSM motor which is based on an extendedelectro-motive force function [13]. This extended electro-motive force (EEMF) model includes both positioninformation from the conventionally defined EMF and thestator inductance as well. Then, it makes possible toobtain the rotor position and velocity information byestimating the extended EMF only.

Fig. 7. Low speed full sensorless FOC, with speed reversal ±30 rpmunder load (20% nominal).

B. High Speed Sensorless ControlThere have been proposed many sensorless control

methods for surface permanent-magnet synchronousmotors based on estimation of electromotive force inwhich the electrical position information of machine isencoded.

[:; R {a]±+PLO{±ke [e(.

Us UR UL UE (7)

±2* L{-sin(20e)) cos(20e)] [ia]

UREL

Fundamentally, these estimation methods for theposition and velocity are based on the motor mathematicalmodel. However, mentioned methods cannot be directlyapplied to an interior permanent-magnet synchronousmotor, because the position information is contained notonly in the conventionally defined back electro-motiveforce (EMF) but also in the definition of stator inductanceas shown in (7).

IIII(Ld-LQL). (Oe][]

PLd 1,

(8)UL

+ ±(Ld Lq ) (t)ebiUE

In this equation (8) there is no 20 dependent termcomparing to conventionally defined IPMSM machinemodel (7). The second term ULEXT and third term UEEXT onthe right side of equation (8) are depicted in Fig. 11 asvectors in dashed yellow lines. The ULEXT vector term inequation (8) can be explained as extension of conventionalinductance voltage drop, and second vector term UEEXT isconsidered as an extension of conventional back EMFterm. It is obvious that extended inductance voltage dropULEXT has no position dependent information and onlyextended back EMF term UEEXT possesses positiondependent information. This rewritten mathematicalmodel of interior PMSM motor makes possible to expressthe extended back EMF term UEEXT to be simply estimatedusing standard estimation approach of surface-mountedPMSM motor.

Uea - sin(F e )Ue/ {(LI -L ) (WCte'Id e Cwe}*L CO o )]

(9)

In eq. (9), besides the conventionally defined EMFgenerated by the permanent magnet, there is a kind ofvoltage related to the saliency of the interior PMSM

1011

i') k e} -0sin(O )

, -axi;saI Us

..i ...9u.||..d

si

motor. It includes the position information from both theEMF and the stator inductance. It is a general form ofmathematical model for all the synchronous motors [13].

C. State Observer ofExtended BackEMFIn this section described state observer is applied to

interior PMSM motor with an estimator model excludingthe extended EMF term. Then extended EMF term can beestimated using the state observer as depicted in Fig. 9,which utilizes a simple observer of IPM motor statorcurrent. Here presented state observer is realized withinstationary reference frame (a,B). The estimator of a-axisconsists of the stator current observer based on RL motorcircuit with estimated motor parameters. This currentobserver is fed by the sum of the actual applied motorvoltage (ua), cross-coupled rotational term whichcorresponds to the motor saliency JL and compensatorFCs,(s) corrective output. Since extended term of backEMF is not included in the interior PMSM motor observermodel, the compensator F,O,(s) corrective output shown inFig. 9 supplies the not modeled extended back EMF[14],[15]. The estimate of extended EMF term in a-axiscan be derived as follows

(10)

It is obvious that the accuracy of the back EMFestimates is determined by the correctness of used motorparameters (R, L) by fidelity of the reference statorvoltage and by quality of compensator such as bandwidth,phase lag and so on. It is obvious from the extended EMFtransfer function that even if motor parameters areprecisely matched, the estimates are limited bycompensator quality. This implies that state observerbandwidth and its corresponding phase lag constraints theperformance of used method. The same consequencesapply for estimate of the extended EMF in P-axis.

The angle tracking observer [16] shown in Fig. 9 iswidely used for the estimation of the rotor angle. Byemploying the tracking observer, noise on the positionestimate can be filtered out without adding lag to theestimate within its bandwidth [14],[16]. The primarybenefit of the angle tracking observer utilization, incomparison with the trigonometric method, is itssmoothing capability [17].

D. Experimetal Results ofExtended BackEMF StateObserverThe extended back EMF state observer has been

implemented using digital signal controller of Freescale's56F8300 series with interior PMSM. The motor withparameters summarized in Table I has been used for theseexperiments.

iEsin Aoh6 Aloh6a ta I astin Beta

~2

-2-

o 7 4 2 3O 40 ~~~~5O6 70

Fig. 10. Estimated a,8 currents by state observer at 300 [rad.sec-1].

Electrical rotor position and speed are fed back fromencoder transducer, and are granted as reference toestimated values of rotor electrical position Oestim andangular speed W)estim. This motor drive operation allowsevaluating the quality of sensorless algorithm. Theobserver tracking capability of phase stator currentsexpressed in stationary reference frame are evaluated asshown in Fig. 10.

Fig. 9. Block diagram of state observer of extended back EMF.

Fig. 11. Estimated extended EMF by state observer at 300[rad.sec-1] andestimated electrical position by angle tracking observer.

The IPM synchronous motor under test have beenoperated in tracking mode, where speed control hasattained the position and speed from encoder, andestimation algorithm tracks actual rotor position. As canbe seen from Fig. 10, the estimation of speed and positionhave very good accuracy and apparently the encoderposition feedback can be replaced by these estimates fromthe extended back EMF state filter. The controller output,which corrects motor phase currents, is supplying part ofthe motor state which is not modelled, i.e. the extendedback EMF. Fig. 11 shows the estimated extended backEMF at 300 [rad.sec-'].

If the IPM synchronous motor drive operates insensorless mode, the electrical position required for vectortransformation is attained from sensorless algorithm andfeedback speed control loop is formed by state observerestimate. Satisfactory sensorless operation was also

1012

I

(s) = F. (s) - I. (s)^

(s)k I.

x

achieved under different operation condition. As can beseen from Fig. 11 there is a very high correspondencebetween estimated rotor position (red) and encodermeasurement of electrical position (blue). The exactknowledge of rotor position is very critical to IPM motorstable operation and it is seen that in sensorless mode theIPM motor functions with minimum sensitivity to motorload having very high agreement of measured positionfrom encoder and state filter estimate.

IPMSM Sensodess Al odfithms

gff~~~~~~sLS

l _ i 8~~O9gvei _ l |~~~etIn_ I ~~~A16ithl~~~~ ~~_ _Es

_--

Fig. 12. Speed control with ramp acceleration under load condition.

Since state observer sensorless algorithm operatesreliable from 50 [rad.sec-'], the speed command isdemanded from this limit. Speed acceleration from50[rad.sec-'] up to 400[rad.sec-'] is shown on Fig. 12. Asis apparent, almost identical behaviour of estimated andencoder speed was achieved. The operation of sensorlessIPM motor drive has also been tested under variable loadcondition as shown in Fig. 13. Here the motor was insteady state and step change in motor load was applied.

55Dmega El Orne-ga El Refeumqne OffiegaEstmnAT(DNIt

4501

Fig. 13. Sensorless speed control at step change in load.

E. Whole Speed Sensorless ControlIn order to fully control IPM synchronous motor

throughout the entire speed range, estimates from low andhigh speed sensorless algorithms have to be evaluated andmerged. Proposed merging algorithm is based on cross-over functions, assuring smooth transition betweenalgorithms. Moreover using cross-over functions allowscompletely switching off the algorithm currently not used[8], thus minimizing losses due to hf injection at highspeeds. Fig. 13 shows block diagram of algorithms forwhole speed sensorless control of IPM synchronousmotor.

Fig. 13. Block diagram ofIPMSM sensorless algorithms for entirespeed range.

Block diagram of IPM synchronous motor fieldoriented control with sensorless position/speed feedback isdepicted on Fig. 14. Fig 15 shows experimental results offull IPM synchronous motor sensorless control obtainedfrom experimental setup according to Fig. 14. In thisexperiment the motor is operated in speed FOC withestimated position/speed provided by merging algorithm.

Fig. 14. Overall structure ofIPMSM sensorless field oriented controlwith speed loop.

Position error is calculated with respect to positionobtained from encoder. Encoder is used only forcomparisons.

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_p"deslte

--I

Fig. 15. Whole speed range full sensorless control with speed reversal.IPMSM operated in speed sensorless FOC.

TABLE I.MOTOR PARAMETERS

MOTOR PARAMETER VALUENumber of poles 20Rated speed 600 [rpm]Phase voltage max. AC 200 [V]Phase current max 8A p-pKe 0.255 [V.sec/rad]Rs 7.5 [Q]Ld 0.081 [H]Lq 0.095 [H]

IV. CONCLUSIONSensorless field oriented control of IPMSM covering

the entire speed range has been presented. Mergingalgorithm based on cross-over function has been designedin order to perform a smooth transition between twodifferent sensorless algorithms. Presented approach by thispaper is based on hfsignal injection method for low speedoperation and on the estimation of an extended EMF inthe stationary reference frame using a state filter for highspeed operation. The spatial information obtained fromthe estimates of extended EMF is used in an angletracking observer to estimate the rotor electrical position.The extended EMF model includes both positioninfornation from the conventionally defined EMF and thestator inductance. This makes it possible to obtain therotor position and velocity information by estimating theextended EMF only. Whole implementation of transientinjection method and extended back EMF state filter hasbeen achieved on a single chip solution of DSC56F8300series without any additional supportive circuitry.

REFERENCES

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